Question: Let $f(x) = -8x^{2}+6x+8$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $-8x^{2}+6x+8 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = -8, b = 6, c = 8$ $ x = \dfrac{-6 \pm \sqrt{6^{2} - 4 \cdot -8 \cdot 8}}{2 \cdot -8}$ $ x = \dfrac{-6 \pm \sqrt{292}}{-16}$ $ x = \dfrac{-6 \pm 2\sqrt{73}}{-16}$ $x =\dfrac{-3 \pm \sqrt{73}}{-8}$